Methods and systems for model predictive control of autonomous driving vehicle

ABSTRACT

Methods and systems for operating an autonomous driving vehicle (ADV) are disclosed. A current state of an ADV is sampled at a first time to obtain a set of parameters. A cost, from a cost function that reflects desired control goals, is generated for a future time horizon based at least in part on the set of parameters. The cost is minimized with one or more constraints to obtain target control input values. For each of the target control input values, a lookup operation is performed using the control input value to locate a first mapping entry that approximately corresponds to the control input value. A first control command is derived from the first mapping entry. The ADV is controlled using the derived first control command.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to operatingautonomous vehicles. More particularly, embodiments of the disclosurerelate to methods and systems for model predictive control of anautonomous driving vehicle.

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieveoccupants, especially the driver, from some driving-relatedresponsibilities. When operating in an autonomous mode, the vehicle cannavigate to various locations using onboard sensors, allowing thevehicle to travel with minimal human interaction or in some caseswithout any passengers.

Motion planning and control are critical operations in autonomousdriving. For example, throttle, brake, and steering commands areimportant commands in autonomous driving. While Model Predictive Control(MPC) has been widely studied for high performance, high precisionrobotic controls, such has been seldomly used (if at all) for autonomousdriving vehicles (ADVs). This is largely due to the excessivecomputational power requirement to implement an MPC model, and theinstability of the MPC model when controlling the ADV in extremeconditions (e.g., large curve, high speed, sharp turn, etc.).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according toone embodiment.

FIG. 2 is a block diagram illustrating an example of an autonomousvehicle according to one embodiment.

FIG. 3 is a block diagram illustrating an example of a perception andplanning system used with an autonomous vehicle according to oneembodiment.

FIG. 4 is a block diagram illustrating an example of a control input tocommand mapping table according to one embodiment of the invention.

FIG. 5 is a flow diagram illustrating a process of operating anautonomous driving vehicle according to one embodiment of the invention.

FIG. 6 is a block diagram illustrating a data processing systemaccording to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be describedwith reference to details discussed below, and the accompanying drawingswill illustrate the various embodiments. The following description anddrawings are illustrative of the disclosure and are not to be construedas limiting the disclosure. Numerous specific details are described toprovide a thorough understanding of various embodiments of the presentdisclosure. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment of the disclosure. The appearances of the phrase “in oneembodiment” in various places in the specification do not necessarilyall refer to the same embodiment.

According to some embodiments, when generating a control command of anADV, such as throttle, brake, or steering control command, a robust MPCmodel may be used to improve performance and maintain stability of theADV. For example, longitudinal vehicle dynamics (e.g., throttle/brakecontrol) may be separated from lateral vehicle dynamics (e.g., steeringcontrol) to control the ADV. For longitudinal control, a throttle/brakecontrol table may be utilized to control the throttle and brakingmaneuvers of the vehicle. For lateral control, a “bicycle model” may becombined with a “tire model” for steering control of the vehicle. In oneembodiment, a linear MPC may be used to perform a close loop control ofthe longitudinal and lateral vehicle dynamics to optimize the drivingcomfort and fuel economy of the vehicle.

In one aspect, a current state of an ADV is sampled at a first time toobtain a set of parameters. A cost, from a cost function that reflectsdesired control goals, is generated for a future time horizon based atleast in part on the set of parameters. The cost is minimized with oneor more constraints to obtain target control input values. For each ofthe target control input values, a lookup operation is performed usingthe control input value to locate a first mapping entry thatapproximately corresponds to the control input value. A first controlcommand is derived from the first mapping entry. The ADV is controlledusing the derived first control command.

In one aspect, for each of the target control input values, the lookupoperation is performed using the control input value to further locate asecond mapping entry that approximately corresponds to the control inputvalue. A second control command is derived from the second mappingentry. The ADV is controlled using the derived second control command.In one embodiment, the first control command is a throttle or brakecommand and the second control command is a steering command. In oneembodiment, the set of parameters includes parameters associated with abicycle model and parameters associated with a tire model. In oneembodiment, minimizing the cost with one or more constraints to obtaintarget control input values includes transforming the cost function to alinear quadratic algorithm, and solving the linear quadratic algorithm.In one embodiment, generation of the cost for a future time horizon isfurther based on one or more weighting values and reference values. Inone embodiment, the target control input values are optimal controlinputs for controlling the ADV over a control window.

FIG. 1 is a block diagram illustrating an autonomous vehicle networkconfiguration according to one embodiment of the disclosure. Referringto FIG. 1, network configuration 100 includes autonomous vehicle 101that may be communicatively coupled to one or more servers 103-104 overa network 102. Although there is one autonomous vehicle shown, multipleautonomous vehicles can be coupled to each other and/or coupled toservers 103-104 over network 102. Network 102 may be any type ofnetworks such as a local area network (LAN), a wide area network (WAN)such as the Internet, a cellular network, a satellite network, or acombination thereof, wired or wireless. Server(s) 103-104 may be anykind of servers or a cluster of servers, such as Web or cloud servers,application servers, backend servers, or a combination thereof. Servers103-104 may be data analytics servers, content servers, trafficinformation servers, map and point of interest (MPOI) severs, orlocation servers, etc.

An autonomous vehicle refers to a vehicle that can be configured to inan autonomous mode in which the vehicle navigates through an environmentwith little or no input from a driver. Such an autonomous vehicle caninclude a sensor system having one or more sensors that are configuredto detect information about the environment in which the vehicleoperates. The vehicle and its associated controller(s) use the detectedinformation to navigate through the environment. Autonomous vehicle 101can operate in a manual mode, a full autonomous mode, or a partialautonomous mode.

In one embodiment, autonomous vehicle 101 includes, but is not limitedto, perception and planning system 110, vehicle control system 111,wireless communication system 112, user interface system 113,infotainment system 114, and sensor system 115. Autonomous vehicle 101may further include certain common components included in ordinaryvehicles, such as, an engine, wheels, steering wheel, transmission,etc., which may be controlled by vehicle control system 111 and/orperception and planning system 110 using a variety of communicationsignals and/or commands, such as, for example, acceleration signals orcommands, deceleration signals or commands, steering signals orcommands, braking signals or commands, etc.

Components 110-115 may be communicatively coupled to each other via aninterconnect, a bus, a network, or a combination thereof. For example,components 110-115 may be communicatively coupled to each other via acontroller area network (CAN) bus. A CAN bus is a vehicle bus standarddesigned to allow microcontrollers and devices to communicate with eachother in applications without a host computer. It is a message-basedprotocol, designed originally for multiplex electrical wiring withinautomobiles, but is also used in many other contexts.

Referring now to FIG. 2, in one embodiment, sensor system 115 includes,but it is not limited to, one or more cameras 211, global positioningsystem (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit214, and a light detection and range (LIDAR) unit 215. GPS system 212may include a transceiver operable to provide information regarding theposition of the autonomous vehicle. IMU unit 213 may sense position andorientation changes of the autonomous vehicle based on inertialacceleration. Radar unit 214 may represent a system that utilizes radiosignals to sense objects within the local environment of the autonomousvehicle. In some embodiments, in addition to sensing objects, radar unit214 may additionally sense the speed and/or heading of the objects.LIDAR unit 215 may sense objects in the environment in which theautonomous vehicle is located using lasers. LIDAR unit 215 could includeone or more laser sources, a laser scanner, and one or more detectors,among other system components. Cameras 211 may include one or moredevices to capture images of the environment surrounding the autonomousvehicle. Cameras 211 may be still cameras and/or video cameras. A cameramay be mechanically movable, for example, by mounting the camera on arotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonarsensor, an infrared sensor, a steering sensor, a throttle sensor, abraking sensor, and an audio sensor (e.g., microphone). An audio sensormay be configured to capture sound from the environment surrounding theautonomous vehicle. A steering sensor may be configured to sense thesteering angle of a steering wheel, wheels of the vehicle, or acombination thereof. A throttle sensor and a braking sensor sense thethrottle position and braking position of the vehicle, respectively. Insome situations, a throttle sensor and a braking sensor may beintegrated as an integrated throttle/braking sensor.

In one embodiment, vehicle control system 111 includes, but is notlimited to, steering unit 201, throttle unit 202 (also referred to as anacceleration unit), and braking unit 203. Steering unit 201 is to adjustthe direction or heading of the vehicle. Throttle unit 202 is to controlthe speed of the motor or engine that in turn control the speed andacceleration of the vehicle. Braking unit 203 is to decelerate thevehicle by providing friction to slow the wheels or tires of thevehicle. Note that the components as shown in FIG. 2 may be implementedin hardware, software, or a combination thereof.

Referring back to FIG. 1, wireless communication system 112 is to allowcommunication between autonomous vehicle 101 and external systems, suchas devices, sensors, other vehicles, etc. For example, wirelesscommunication system 112 can wirelessly communicate with one or moredevices directly or via a communication network, such as servers 103-104over network 102. Wireless communication system 112 can use any cellularcommunication network or a wireless local area network (WLAN), e.g.,using WiFi to communicate with another component or system. Wirelesscommunication system 112 could communicate directly with a device (e.g.,a mobile device of a passenger, a display device, a speaker withinvehicle 101), for example, using an infrared link, Bluetooth, etc. Userinterface system 113 may be part of peripheral devices implementedwithin vehicle 101 including, for example, a keyword, a touch screendisplay device, a microphone, and a speaker, etc.

Some or all of the functions of autonomous vehicle 101 may be controlledor managed by perception and planning system 110, especially whenoperating in an autonomous driving mode. Perception and planning system110 includes the necessary hardware (e.g., processor(s), memory,storage) and software (e.g., operating system, planning and routingprograms) to receive information from sensor system 115, control system111, wireless communication system 112, and/or user interface system113, process the received information, plan a route or path from astarting point to a destination point, and then drive vehicle 101 basedon the planning and control information. Alternatively, perception andplanning system 110 may be integrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and adestination of a trip, for example, via a user interface. Perception andplanning system 110 obtains the trip related data. For example,perception and planning system 110 may obtain location and routeinformation from an MPOI server, which may be a part of servers 103-104.The location server provides location services and the MPOI serverprovides map services and the POIs of certain locations. Alternatively,such location and MPOI information may be cached locally in a persistentstorage device of perception and planning system 110.

While autonomous vehicle 101 is moving along the route, perception andplanning system 110 may also obtain real-time traffic information from atraffic information system or server (TIS). Note that servers 103-104may be operated by a third party entity. Alternatively, thefunctionalities of servers 103-104 may be integrated with perception andplanning system 110. Based on the real-time traffic information, MPOIinformation, and location information, as well as real-time localenvironment data detected or sensed by sensor system 115 (e.g.,obstacles, objects, nearby vehicles), perception and planning system 110can plan an optimal route and drive vehicle 101, for example, viacontrol system 111, according to the planned route to reach thespecified destination safely and efficiently.

Server 103 may be a data analytics system to perform data analyticsservices for a variety of clients. In one embodiment, data analyticssystem 103 includes data collector 121 and machine learning engine 122.Data collector 121 collects driving statistics 123 from a variety ofvehicles, either autonomous vehicles or regular vehicles driven by humandrivers. Driving statistics 123 include information indicating thedriving commands (e.g., throttle, brake, steering commands) issued andresponses of the vehicles (e.g., speeds, accelerations, decelerations,directions) captured by sensors of the vehicles at different points intime. Driving statistics 123 may further include information describingthe driving environments at different points in time, such as, forexample, routes (including starting and destination locations), MPOIs,road conditions, weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generatesor trains a set of rules, algorithms, and/or predictive models 124 for avariety of purposes. In one embodiment, machine learning engine 122analyzes driving statistics 123 and generates command table 125 for avariety of vehicles (e.g., autonomous vehicle 101). The command table125 includes a number of mapping entries. Each mapping entry maps aparticular optimal input of a prediction model to one or more controlcommands (e.g., throttle/brake command, steering command). Note thatdifferent command tables may be configured for multiple types ofvehicles. Command table 125 may be uploaded onto ADVs to be used inreal-time for autonomous driving of the ADVs.

Alternatively, the command table 125 may be implemented as a machinelearning predictive or determination model. The inputs provided to thepredictive or determination model can include parameters associated witha bicycle model and tire model, such as lateral displacement, rate ofchange of lateral displacement, heading angle, rate of change of headingangle, difference between expected and actual driving distances, rate ofchange of the difference between expected and actual driving distances,a cornering stiffness of front tires of the vehicle, a corneringstiffness of rear tires of the vehicle, a longitudinal distance from acenter of gravity to the front tires, a longitudinal distance from acenter of gravity to the rear tires, a vehicle mass, a steering angle ofthe vehicle, acceleration of the vehicle, reference in acceleration,and/or longitudinal turning radius, and outputs of the model can betarget control inputs used to obtain control commands (e.g.,throttle/brake command and steering command).

FIG. 3 is a block diagram illustrating an example of a perception andplanning system used with an autonomous vehicle according to oneembodiment. System 300 may be implemented as a part of autonomousvehicle 101 of FIG. 1 including, but is not limited to, perception andplanning system 110, control system 111, and sensor system 115.Referring to FIGS. 3A-3B, perception and planning system 110 includes,but is not limited to, localization module 301, perception module 302,prediction module 303, decision module 304, planning module 305, controlmodule 306, routing module 307, and model predictive control (MPC)module 308.

Some or all of modules 301-308 may be implemented in software, hardware,or a combination thereof. For example, these modules may be installed inpersistent storage device 352, loaded into memory 351, and executed byone or more processors (not shown). Note that some or all of thesemodules may be communicatively coupled to or integrated with some or allmodules of vehicle control system 111 of FIG. 2. Some of modules 301-308may be integrated together as an integrated module. For example, MPCmodule 308 may be integrated with control module 306 and/or planningmodule 305.

Localization module 301 determines a current location of autonomousvehicle 300 (e.g., leveraging GPS unit 212) and manages any data relatedto a trip or route of a user. Localization module 301 (also referred toas a map and route module) manages any data related to a trip or routeof a user. A user may log in and specify a starting location and adestination of a trip, for example, via a user interface. Localizationmodule 301 communicates with other components of autonomous vehicle 300,such as map and route information 311, to obtain the trip related data.For example, localization module 301 may obtain location and routeinformation from a location server and a map and POI (MPOI) server. Alocation server provides location services and an MPOI server providesmap services and the POIs of certain locations, which may be cached aspart of map and route information 311. While autonomous vehicle 300 ismoving along the route, localization module 301 may also obtainreal-time traffic information from a traffic information system orserver.

Based on the sensor data provided by sensor system 115 and localizationinformation obtained by localization module 301, a perception of thesurrounding environment is determined by perception module 302. Theperception information may represent what an ordinary driver wouldperceive surrounding a vehicle in which the driver is driving. Theperception can include the lane configuration (e.g., straight or curvelanes), traffic light signals, a relative position of another vehicle, apedestrian, a building, crosswalk, or other traffic related signs (e.g.,stop signs, yield signs), etc., for example, in a form of an object.

Perception module 302 may include a computer vision system orfunctionalities of a computer vision system to process and analyzeimages captured by one or more cameras in order to identify objectsand/or features in the environment of autonomous vehicle. The objectscan include traffic signals, road way boundaries, other vehicles,pedestrians, and/or obstacles, etc. The computer vision system may usean object recognition algorithm, video tracking, and other computervision techniques. In some embodiments, the computer vision system canmap an environment, track objects, and estimate the speed of objects,etc. Perception module 302 can also detect objects based on othersensors data provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts what the objectwill behave under the circumstances. The prediction is performed basedon the perception data perceiving the driving environment at the pointin time in view of a set of map/rout information 311 and traffic rules312. For example, if the object is a vehicle at an opposing directionand the current driving environment includes an intersection, predictionmodule 303 will predict whether the vehicle will likely move straightforward or make a turn. If the perception data indicates that theintersection has no traffic light, prediction module 303 may predictthat the vehicle may have to fully stop prior to enter the intersection.If the perception data indicates that the vehicle is currently at aleft-turn only lane or a right-turn only lane, prediction module 303 maypredict that the vehicle will more likely make a left turn or right turnrespectively.

For each of the objects, decision module 304 makes a decision regardinghow to handle the object. For example, for a particular object (e.g.,another vehicle in a crossing route) as well as its metadata describingthe object (e.g., a speed, direction, turning angle), decision module304 decides how to encounter the object (e.g., overtake, yield, stop,pass). Decision module 304 may make such decisions according to a set ofrules such as traffic rules or driving rules 312, which may be stored inpersistent storage device 352.

Routing module 307 is configured to provide one or more routes or pathsfrom a starting point to a destination point. For a given trip from astart location to a destination location, for example, received from auser, routing module 307 obtains route and map information 311 anddetermines all possible routes or paths from the starting location toreach the destination location. Routing module 307 may generate areference line in a form of a topographic map for each of the routes itdetermines from the starting location to reach the destination location.A reference line refers to an ideal route or path without anyinterference from others such as other vehicles, obstacles, or trafficcondition. That is, if there is no other vehicle, pedestrians, orobstacles on the road, an ADV should exactly or closely follows thereference line. The topographic maps are then provided to decisionmodule 304 and/or planning module 305. Decision module 304 and/orplanning module 305 examine all of the possible routes to select andmodify one of the most optimal route in view of other data provided byother modules such as traffic conditions from localization module 301,driving environment perceived by perception module 302, and trafficcondition predicted by prediction module 303. The actual path or routefor controlling the ADV may be close to or different from the referenceline provided by routing module 307 dependent upon the specific drivingenvironment at the point in time.

Based on a decision for each of the objects perceived, planning module305 plans a path or route for the autonomous vehicle, as well as drivingparameters (e.g., distance, speed, and/or turning angle), using areference line provided by routing module 307 as a basis. That is, for agiven object, decision module 304 decides what to do with the object,while planning module 305 determines how to do it. For example, for agiven object, decision module 304 may decide to pass the object, whileplanning module 305 may determine whether to pass on the left side orright side of the object. Planning and control data is generated byplanning module 305 including information describing how vehicle 300would move in a next moving cycle (e.g., next route/path segment). Forexample, the planning and control data may instruct vehicle 300 to move10 meters at a speed of 30 mile per hour (mph), then change to a rightlane at the speed of 25 mph.

Based on the planning and control data, control module 306 controls anddrives the autonomous vehicle, by sending proper commands or signals tovehicle control system 111, according to a route or path defined by theplanning and control data. The planning and control data includesufficient information to drive the vehicle from a first point to asecond point of a route or path using appropriate vehicle settings ordriving parameters (e.g., throttle, braking, and turning commands) atdifferent points in time along the path or route.

In one embodiment, the planning phase is performed in a number ofplanning cycles, also referred to as command cycles, such as, forexample, in every time interval of 100 milliseconds (ms). For each ofthe planning cycles or command cycles, one or more control commands willbe issued based on the planning and control data. That is, for every 100ms, planning module 305 plans a next route segment or path segment, forexample, including a target position and the time required for the ADVto reach the target position. Alternatively, planning module 305 mayfurther specify the specific speed, direction, and/or steering angle,etc. In one embodiment, planning module 305 plans a route segment orpath segment for the next predetermined period of time such as 5seconds. For each planning cycle, planning module 305 plans a targetposition for the current cycle (e.g., next 5 seconds) based on a targetposition planned in a previous cycle. Control module 306 then generatesone or more control commands (e.g., throttle, brake, steering controlcommands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integratedas an integrated module. Decision module 304/planning module 305 mayinclude a navigation system or functionalities of a navigation system todetermine a driving path for the autonomous vehicle. For example, thenavigation system may determine a series of speeds and directionalheadings to effect movement of the autonomous vehicle along a path thatsubstantially avoids perceived obstacles while generally advancing theautonomous vehicle along a roadway-based path leading to an ultimatedestination. The destination may be set according to user inputs viauser interface system 113. The navigation system may update the drivingpath dynamically while the autonomous vehicle is in operation. Thenavigation system can incorporate data from a GPS system and one or moremaps so as to determine the driving path for the autonomous vehicle.

Decision module 304/planning module 305 may further include a collisionavoidance system or functionalities of a collision avoidance system toidentify, evaluate, and avoid or otherwise negotiate potential obstaclesin the environment of the autonomous vehicle. For example, the collisionavoidance system may effect changes in the navigation of the autonomousvehicle by operating one or more subsystems in control system 111 toundertake swerving maneuvers, turning maneuvers, braking maneuvers, etc.The collision avoidance system may automatically determine feasibleobstacle avoidance maneuvers on the basis of surrounding trafficpatterns, road conditions, etc. The collision avoidance system may beconfigured such that a swerving maneuver is not undertaken when othersensor systems detect vehicles, construction barriers, etc. in theregion adjacent the autonomous vehicle that would be swerved into. Thecollision avoidance system may automatically select the maneuver that isboth available and maximizes safety of occupants of the autonomousvehicle. The collision avoidance system may select an avoidance maneuverpredicted to cause the least amount of acceleration in a passenger cabinof the autonomous vehicle.

According to one embodiment, when control module 306 determines acontrol command to be issued to the ADV, control module 306 may invokeMPC module 308 to obtain control inputs, which are used to obtaindifferent control commands (e.g., throttle/braking commands, steeringcommands). MPC module 308 may apply an MPC model (e.g., a combination ofbicycle model and tire model) to determine optimal control inputs withina control window or interval. An MPC model is an optimal-control basedmethod to select control inputs by minimizing an objective function. Theobjective function may be defined in terms of both present and predictedsystem variables and may be evaluated using an explicit model to predictfuture outputs.

For example, in one embodiment, MPC module 308 may determine the statesfor a control loop based on the relationships:

{dot over (x)}=Ax+Bu+C

with,

${x = \begin{bmatrix}e_{d} \\{\overset{.}{e}}_{d} \\e_{\theta} \\{\overset{.}{e}}_{\theta} \\e_{s} \\{\overset{.}{e}}_{s}\end{bmatrix}},$

where parameters e_(d) is a lateral displacement, ė_(d) is a rate ofchange of the lateral displacement, e_(θ) is a heading angle, ė_(θ) is arate of change of the heading angle, e_(s) is a difference betweenexpected and actual driving distances, and ė_(s) is a rate of change ofthe difference between expected and actual driving distances,

$A = \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\0 & \frac{- \left( {c_{f} + c_{r}} \right)}{{mv}_{x}} & \frac{c_{f} + c_{r}}{m} & \frac{{l_{f}c_{f}} - {l_{r}c_{r}}}{{mv}_{x}} & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & \frac{{l_{r}c_{r}} - {l_{f}c_{f}}}{I_{z}v_{x}} & \frac{{l_{f}c_{f}} - {l_{r}c_{r}}}{I_{z}} & \frac{- \left( {{l_{f}^{2}c_{f}} + {l_{r}^{2}c_{r}}} \right)}{I_{z}v_{x}} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ ${B = \begin{bmatrix}0 & 0 \\\frac{c_{f}}{m} & 0 \\0 & 0 \\\frac{I_{f}c_{f}}{I_{z}} & 0 \\0 & 0 \\0 & {- 1}\end{bmatrix}},{u = \begin{bmatrix}\delta \\\alpha\end{bmatrix}},{C = {\begin{bmatrix}0 & 0 \\{\frac{{l_{r}c_{r}} - {l_{f}c_{f}}}{{mv}_{x}} - v_{x}} & 0 \\0 & 0 \\\frac{- \left( {{l_{r}^{2}c_{r}} + {l_{f}^{2}c_{f}}} \right)}{I_{z}v_{x}} & 0 \\0 & 0 \\0 & 1\end{bmatrix}\begin{bmatrix}\overset{.}{\gamma} \\\alpha_{ref}\end{bmatrix}}},{\overset{.}{\gamma} = {\frac{v_{x}}{R_{x}} = v_{x\; {curvature}}}}\;,$

where parameters c_(f) is a cornering stiffness of front tires of thevehicle, c_(r) is a cornering stiffness of rear tires of the vehicle,l_(f) is a longitudinal distance from a center of gravity to the fronttires, l_(r) is a longitudinal distance from the center of gravity tothe rear tires, m is a vehicle mass, v_(x) is a longitudinal velocity ofthe vehicle, I_(z) is a yaw moment of inertia of the vehicle, δ is asteering angle of the vehicle, a is acceleration of the vehicle, a_(ref)is a reference in acceleration, and R_(x) is a longitudinal turningradius.

From the continuous relationships described above, the followingdiscrete relationships can be obtained:

x(k+1)=A_(d)x(k)+B_(d)u(k)+C_(d), where k is a k-th control loop, x(k+1)is a vector with entries indicative of states of the vehicle for the(k+1)-th control loop, x(k) is the vector x(k+1) from the k-th controlloop, A_(d) is a matrix including constant values calibrated based oncharacteristics of the vehicle (e.g., characteristics provided byperception and planning system 110 as previously described), B_(d) is amatrix including constant values calibrated based on characteristics ofthe vehicle, u(k) is a control vector for the k-th control loop, andC_(d) is a matrix including constant values calibrated based oncharacteristics of the vehicle.

Accordingly, if the control window is set to N, where N is an integergreater than 1, in discrete domain the equation is written as follows:

${{X(N)} = {{\Psi \; {X(k)}} + {\Theta \; {U(N)}} + H}},{{{with}\mspace{14mu} {X(N)}} = \begin{bmatrix}{x\left( {k + 1} \right)} \\{x\left( {k + 2} \right)} \\{x\left( {k + 3} \right)} \\\ldots \\{x\left( {k + N} \right)}\end{bmatrix}},{\Psi = \begin{bmatrix}A_{d} \\A_{d}^{2} \\A_{d}^{3} \\\ldots \\A_{d}^{N}\end{bmatrix}},{\Theta = \begin{bmatrix}B_{d} & 0 & 0 & \ldots & 0 \\{A_{d}B_{d}} & B_{d} & 0 & \ldots & 0 \\{A_{d}^{2}B_{d}} & {A_{d}B_{d}} & B_{d} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\{A_{d}^{N - 1}B_{d}} & {A_{d}^{N - 2}B_{d}} & {A_{d}^{N - 3}B_{d}} & \ldots & B_{d}\end{bmatrix}},{H = \begin{bmatrix}C_{d} \\{{A_{d}C_{d}} + C_{d}} \\{{A_{d}^{2}C_{d}} + {A_{d}C_{d}} + C_{d}} \\\ldots \\{{A_{d}^{N - 1}C_{d}} + {A_{d}^{N - 2}C_{d}} + \ldots + C_{d}}\end{bmatrix}},{{U(N)} = {\begin{bmatrix}{u(k)} \\{u\left( {k + 1} \right)} \\{u\left( {k + 2} \right)} \\\ldots \\{u\left( {k + N - 1} \right)}\end{bmatrix}.}}$

Next, optimal values for time k can be calculated to minimize a cost (orobjective) function during the period from the time k=0 to the time k=N,where N is an integer greater than 1. The cost function is theperformance criterion to be minimized in the optimal control problemdefined over a predictive time horizon in the future. That is, the costfunction reflects the desired control goals. For example, consider thefollowing cost function:

${J = {{\sum\limits_{i = 1}^{N}{{{x\left( {i + 1} \right)} - {x_{ref}\left( {i + 1} \right)}}}_{Q}} + {\sum\limits_{i = 1}^{N - 1}{{u\left( {i + 1} \right)}}_{R}^{2}}}},$

where Q and R are weighting matrices of approximate dimensions,

With the above cost function, the first objective is to maintaintracking accuracy and the second objective is to minimize controlchanges. The cost function depends on the manipulated variable u and itsvariation u(i+1), which are the desired (or target) control inputvalues. Accordingly, the following lower and upper constraints may beapplied to select the target control input values:

u _(min)(k+i)≤u(k+i)≤u _(max)(k+i),i=0,1, . . . ,N−1.

The equation above can be written in discrete domain as follows:

J=U(N)^(T) ΦU(N)+2U(N)^(T) G,

where Φ=Θ^(T)QΘ+R, G=Θ^(T) QE, E=ΨX(K)+H−X_(ref) (N).

Equivalently, the above equation can be transferred or transformed tolinear quadratic equations as follows:

min J=U(N)^(T) ΦU(N)+2U(N)^(T) G

s.t. U _(min)(N)≤U(N)≤U _(max)(N)

Such linear quadratic equations can be solved to result in:

U_(N)*[u_(k)*, u_(k+1)*, u_(k+2)*, . . . , u_(k+n−1)*]^(T), where eachvariable u may serve as an optimal control input to obtain a controlcommand (e.g., throttle/braking command, steering command) within acontrol window, for example from sample time k=0 to the time k=N, whereN is an integer greater than 1.

For instance, based on a particular control input 451, MPC module 308may look up in command table 125, for example as shown in FIG. 4, tolocate a first mapping entry (e.g., field 452) and a second mappingentry (e.g., field 453) that approximately or exactly match (orcorrespond) the control input u. Based on the first mapping entry andthe second mapping entry, control module 305 may determine a finalcontrol command (e.g., throttle/brake command, steering command), wherethe final control command is issued to drive the ADV. As the finalcontrol command is determined for each sample time k=0 to time k=N,optimal driving comfort and fuel economy may be achieved from the ADV.

FIG. 5 is a flow diagram illustrating a process of operating anautonomous driving vehicle according to one embodiment of the invention.Process 500 may be performed by processing logic which may includesoftware, hardware, or a combination thereof. For example, process 500may be performed by control module 306 and/or MPC module 308 of FIG. 3.

Referring to FIG. 5, in operation 501, the processing logic samples acurrent state of an autonomous driving vehicle (ADV) at a first time(e.g., time k=0) to obtain a set of parameters (e.g., e_(d), ė_(d),e_(θ), ė_(s), e_(s), ė_(s), c_(f), c_(r), l_(f), l_(r), m, I_(z), δ, a,a_(ref), R_(x)). In operation 502, the processing logic generates acost, from a cost function that reflects desired control goals, for afuture time horizon (e.g., time k=1 to the time k=N) based at least inpart on the set of parameters. In operation 503, the processing logicminimizes the cost with one or more constraints to obtain target controlinput values. For each of the target control input values, in operation504, the processing logic performs a lookup operation using the controlinput value to locate a first mapping entry that approximatelycorresponds to the control input value. In operation 505, the processinglogic derives a first control command from the first mapping entry. Inoperation 506, the processing logic controls the ADV using the derivedfirst control command.

Note that some or all of the components as shown and described above maybe implemented in software, hardware, or a combination thereof. Forexample, such components can be implemented as software installed andstored in a persistent storage device, which can be loaded and executedin a memory by a processor (not shown) to carry out the processes oroperations described throughout this application. Alternatively, suchcomponents can be implemented as executable code programmed or embeddedinto dedicated hardware such as an integrated circuit (e.g., anapplication specific IC or ASIC), a digital signal processor (DSP), or afield programmable gate array (FPGA), which can be accessed via acorresponding driver and/or operating system from an application.Furthermore, such components can be implemented as specific hardwarelogic in a processor or processor core as part of an instruction setaccessible by a software component via one or more specificinstructions.

FIG. 6 is a block diagram illustrating an example of a data processingsystem which may be used with one embodiment of the disclosure. Forexample, system 1500 may represent any of data processing systemsdescribed above performing any of the processes or methods describedabove, such as, for example, perception and planning system 110 or anyof servers 103-104 of FIG. 1. System 1500 can include many differentcomponents. These components can be implemented as integrated circuits(ICs), portions thereof, discrete electronic devices, or other modulesadapted to a circuit board such as a motherboard or add-in card of thecomputer system, or as components otherwise incorporated within achassis of the computer system.

Note also that system 1500 is intended to show a high level view of manycomponents of the computer system. However, it is to be understood thatadditional components may be present in certain implementations andfurthermore, different arrangement of the components shown may occur inother implementations. System 1500 may represent a desktop, a laptop, atablet, a server, a mobile phone, a media player, a personal digitalassistant (PDA), a Smartwatch, a personal communicator, a gaming device,a network router or hub, a wireless access point (AP) or repeater, aset-top box, or a combination thereof. Further, while only a singlemachine or system is illustrated, the term “machine” or “system” shallalso be taken to include any collection of machines or systems thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein.

In one embodiment, system 1500 includes processor 1501, memory 1503, anddevices 1505-1508 connected via a bus or an interconnect 1510. Processor1501 may represent a single processor or multiple processors with asingle processor core or multiple processor cores included therein.Processor 1501 may represent one or more general-purpose processors suchas a microprocessor, a central processing unit (CPU), or the like. Moreparticularly, processor 1501 may be a complex instruction set computing(CISC) microprocessor, reduced instruction set computing (RISC)microprocessor, very long instruction word (VLIW) microprocessor, orprocessor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processor 1501 may alsobe one or more special-purpose processors such as an applicationspecific integrated circuit (ASIC), a cellular or baseband processor, afield programmable gate array (FPGA), a digital signal processor (DSP),a network processor, a graphics processor, a communications processor, acryptographic processor, a co-processor, an embedded processor, or anyother type of logic capable of processing instructions.

Processor 1501, which may be a low power multi-core processor socketsuch as an ultra-low voltage processor, may act as a main processingunit and central hub for communication with the various components ofthe system. Such processor can be implemented as a system on chip (SoC).Processor 1501 is configured to execute instructions for performing theoperations and steps discussed herein. System 1500 may further include agraphics interface that communicates with optional graphics subsystem1504, which may include a display controller, a graphics processor,and/or a display device.

Processor 1501 may communicate with memory 1503, which in one embodimentcan be implemented via multiple memory devices to provide for a givenamount of system memory. Memory 1503 may include one or more volatilestorage (or memory) devices such as random access memory (RAM), dynamicRAM (DRAM), synchronous DRAM (SDRAM), static RAM (SRAM), or other typesof storage devices. Memory 1503 may store information includingsequences of instructions that are executed by processor 1501, or anyother device. For example, executable code and/or data of a variety ofoperating systems, device drivers, firmware (e.g., input output basicsystem or BIOS), and/or applications can be loaded in memory 1503 andexecuted by processor 1501. An operating system can be any kind ofoperating systems, such as, for example, Robot Operating System (ROS),Windows® operating system from Microsoft®, Mac OS®/iOS® from Apple,Android® from Google®, LINUX, UNIX, or other real-time or embeddedoperating systems.

System 1500 may further include 10 devices such as devices 1505-1508,including network interface device(s) 1505, optional input device(s)1506, and other optional 10 device(s) 1507. Network interface device1505 may include a wireless transceiver and/or a network interface card(NIC). The wireless transceiver may be a WiFi transceiver, an infraredtransceiver, a Bluetooth transceiver, a WiMax transceiver, a wirelesscellular telephony transceiver, a satellite transceiver (e.g., a globalpositioning system (GPS) transceiver), or other radio frequency (RF)transceivers, or a combination thereof. The NIC may be an Ethernet card.

Input device(s) 1506 may include a mouse, a touch pad, a touch sensitivescreen (which may be integrated with display device 1504), a pointerdevice such as a stylus, and/or a keyboard (e.g., physical keyboard or avirtual keyboard displayed as part of a touch sensitive screen). Forexample, input device 1506 may include a touch screen controller coupledto a touch screen. The touch screen and touch screen controller can, forexample, detect contact and movement or break thereof using any of aplurality of touch sensitivity technologies, including but not limitedto capacitive, resistive, infrared, and surface acoustic wavetechnologies, as well as other proximity sensor arrays or other elementsfor determining one or more points of contact with the touch screen.

IO devices 1507 may include an audio device. An audio device may includea speaker and/or a microphone to facilitate voice-enabled functions,such as voice recognition, voice replication, digital recording, and/ortelephony functions. Other IO devices 1507 may further include universalserial bus (USB) port(s), parallel port(s), serial port(s), a printer, anetwork interface, a bus bridge (e.g., a PCI-PCI bridge), sensor(s)(e.g., a motion sensor such as an accelerometer, gyroscope, amagnetometer, a light sensor, compass, a proximity sensor, etc.), or acombination thereof. Devices 1507 may further include an imagingprocessing subsystem (e.g., a camera), which may include an opticalsensor, such as a charged coupled device (CCD) or a complementarymetal-oxide semiconductor (CMOS) optical sensor, utilized to facilitatecamera functions, such as recording photographs and video clips. Certainsensors may be coupled to interconnect 1510 via a sensor hub (notshown), while other devices such as a keyboard or thermal sensor may becontrolled by an embedded controller (not shown), dependent upon thespecific configuration or design of system 1500.

To provide for persistent storage of information such as data,applications, one or more operating systems and so forth, a mass storage(not shown) may also couple to processor 1501. In various embodiments,to enable a thinner and lighter system design as well as to improvesystem responsiveness, this mass storage may be implemented via a solidstate device (SSD). However in other embodiments, the mass storage mayprimarily be implemented using a hard disk drive (HDD) with a smalleramount of SSD storage to act as a SSD cache to enable non-volatilestorage of context state and other such information during power downevents so that a fast power up can occur on re-initiation of systemactivities. Also a flash device may be coupled to processor 1501, e.g.,via a serial peripheral interface (SPI). This flash device may providefor non-volatile storage of system software, including BIOS as well asother firmware of the system.

Storage device 1508 may include computer-accessible storage medium 1509(also known as a machine-readable storage medium or a computer-readablemedium) on which is stored one or more sets of instructions or software(e.g., module, unit, and/or logic 1528) embodying any one or more of themethodologies or functions described herein. Processingmodule/unit/logic 1528 may represent any of the components describedabove, such as, for example, planning module 305, control module 306,and MPC module 308. Processing module/unit/logic 1528 may also reside,completely or at least partially, within memory 1503 and/or withinprocessor 1501 during execution thereof by data processing system 1500,memory 1503 and processor 1501 also constituting machine-accessiblestorage media. Processing module/unit/logic 1528 may further betransmitted or received over a network via network interface device1505.

Computer-readable storage medium 1509 may also be used to store the somesoftware functionalities described above persistently. Whilecomputer-readable storage medium 1509 is shown in an exemplaryembodiment to be a single medium, the term “computer-readable storagemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The terms“computer-readable storage medium” shall also be taken to include anymedium that is capable of storing or encoding a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the present disclosure. The term“computer-readable storage medium” shall accordingly be taken toinclude, but not be limited to, solid-state memories, and optical andmagnetic media, or any other non-transitory machine-readable medium.

Processing module/unit/logic 1528, components and other featuresdescribed herein can be implemented as discrete hardware components orintegrated in the functionality of hardware components such as ASICS,FPGAs, DSPs or similar devices. In addition, processingmodule/unit/logic 1528 can be implemented as firmware or functionalcircuitry within hardware devices. Further, processing module/unit/logic1528 can be implemented in any combination hardware devices and softwarecomponents.

Note that while system 1500 is illustrated with various components of adata processing system, it is not intended to represent any particulararchitecture or manner of interconnecting the components; as suchdetails are not germane to embodiments of the present disclosure. Itwill also be appreciated that network computers, handheld computers,mobile phones, servers, and/or other data processing systems which havefewer components or perhaps more components may also be used withembodiments of the disclosure.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as those set forth in the claims below, refer to the actionand processes of a computer system, or similar electronic computingdevice, that manipulates and transforms data represented as physical(electronic) quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performingthe operations herein. Such a computer program is stored in anon-transitory computer readable medium. A machine-readable mediumincludes any mechanism for storing information in a form readable by amachine (e.g., a computer). For example, a machine-readable (e.g.,computer-readable) medium includes a machine (e.g., a computer) readablestorage medium (e.g., read only memory (“ROM”), random access memory(“RAM”), magnetic disk storage media, optical storage media, flashmemory devices).

The processes or methods depicted in the preceding figures may beperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software (e.g., embodied on a non-transitorycomputer readable medium), or a combination of both. Although theprocesses or methods are described above in terms of some sequentialoperations, it should be appreciated that some of the operationsdescribed may be performed in a different order. Moreover, someoperations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with referenceto any particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have beendescribed with reference to specific exemplary embodiments thereof. Itwill be evident that various modifications may be made thereto withoutdeparting from the broader spirit and scope of the disclosure as setforth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A computer-implemented method for operating anautonomous driving vehicle, the method comprising: sampling a currentstate of an autonomous driving vehicle (ADV) at a first time to obtain aset of parameters; generating a cost, from a cost function that reflectsdesired control goals, for a future time horizon based at least in parton the set of parameters; minimizing the cost with one or moreconstraints to obtain target control input values; and for each of thetarget control input values, performing a lookup operation using thecontrol input value to locate a first mapping entry that approximatelycorresponds to the control input value, deriving a first control commandfrom the first mapping entry, and controlling the ADV using the derivedfirst control command.
 2. The method of claim 1, further comprising: foreach of the target control input values, performing the lookup operationusing the control input value to further locate a second mapping entrythat approximately corresponds to the control input value, deriving asecond control command from the second mapping entry, and controllingthe ADV using the derived second control command.
 3. The method of claim2, wherein the first control command is a throttle or brake command, andthe second control command is a steering command.
 4. The method of claim1, wherein the set of parameters includes parameters associated with abicycle model and parameters associated with a tire model.
 5. The methodof claim 1, wherein minimizing the cost with one or more constraints toobtain target control input values comprises transforming the costfunction to a linear quadratic algorithm, and solving the linearquadratic algorithm.
 6. The method of claim 1, wherein generating a costfor a future time horizon is further based on one or more weightingvalues and reference values.
 7. The method of claim 1, wherein thetarget control input values are optimal control inputs for controllingthe ADV over a control window.
 8. A non-transitory machine-readablemedium having instructions stored therein, which when executed by aprocessor, cause the processor to perform operations, the operationscomprising: sampling a current state of an autonomous driving vehicle(ADV) at a first time to obtain a set of parameters; generating a cost,from a cost function that reflects desired control goals, for a futuretime horizon based at least in part on the set of parameters; minimizingthe cost with one or more constraints to obtain target control inputvalues; and for each of the target control input values, performing alookup operation using the control input value to locate a first mappingentry that approximately corresponds to the control input value,deriving a first control command from the first mapping entry, andcontrolling the ADV using the derived first control command.
 9. Thenon-transitory machine-readable medium of claim 8, wherein theoperations further comprise: for each of the target control inputvalues, performing the lookup operation using the control input value tofurther locate a second mapping entry that approximately corresponds tothe control input value, deriving a second control command from thesecond mapping entry, and controlling the ADV using the derived secondcontrol command.
 10. The non-transitory machine-readable medium of claim9, wherein the first control command is a throttle or brake command, andthe second control command is a steering command.
 11. The non-transitorymachine-readable medium of claim 8, wherein the set of parametersincludes parameters associated with a bicycle model and parametersassociated with a tire model.
 12. The non-transitory machine-readablemedium of claim 8, wherein minimizing the cost with one or moreconstraints to obtain target control input values comprises transformingthe cost function to a linear quadratic algorithm, and solving thelinear quadratic algorithm.
 13. The non-transitory machine-readablemedium of claim 8, wherein generating a cost for a future time horizonis further based on one or more weighting values and reference values.14. The non-transitory machine-readable medium of claim 8, wherein thetarget control input values are optimal control inputs for controllingthe ADV over a control window.
 15. A data processing system, comprising:a processor; and a memory coupled to the processor to storeinstructions, which when executed by the processor, cause the processorto perform operations, the operations including sampling a current stateof an autonomous driving vehicle (ADV) at a first time to obtain a setof parameters; generating a cost, from a cost function that reflectsdesired control goals, for a future time horizon based at least in parton the set of parameters; minimizing the cost with one or moreconstraints to obtain target control input values; and for each of thetarget control input values, performing a lookup operation using thecontrol input value to locate a first mapping entry that approximatelycorresponds to the control input value, deriving a first control commandfrom the first mapping entry, and controlling the ADV using the derivedfirst control command.
 16. The data processing system of claim 15,wherein the operations further include: for each of the target controlinput values, performing the lookup operation using the control inputvalue to further locate a second mapping entry that approximatelycorresponds to the control input value, deriving a second controlcommand from the second mapping entry, and controlling the ADV using thederived second control command.
 17. The data processing system of claim16, wherein the first control command is a throttle or brake command,and the second control command is a steering command.
 18. The dataprocessing system of claim 15, wherein the set of parameters includesparameters associated with a bicycle model and parameters associatedwith a tire model.
 19. The data processing system of claim 15, whereinminimizing the cost with one or more constraints to obtain targetcontrol input values comprises transforming the cost function to alinear quadratic algorithm, and solving the linear quadratic algorithm.20. The data processing system of claim 15, wherein generating a costfor a future time horizon is further based on one or more weightingvalues and reference values.
 21. The data processing system of claim 15,wherein the target control input values are optimal control inputs forcontrolling the ADV over a control window.